For the oscillating bob of a pendulum, kinetic energy is at its minimum at the maximum height. Which statement is true, accordin
g to the Work-Energy theorem?
A) Maximum work is done on the bob between points A and C.
B) Minimum work is done on the bob between points B and C.
C) Maximum work is done on the bob between points A and B.
D) Minimum work is done on the bob between points A and B.
A) Maximum work is done on the bob between points A and C.
B) Minimum work is done on the bob between points B and C.
C) Maximum work is done on the bob between points A and B.
D) Minimum work is done on the bob between points A and B.
1 answer:
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Answer:
a) t=24s
b) number of oscillations= 11
Explanation:
In case of a damped simple harmonic oscillator the equation of motion is
m(d²x/dt²)+b(dx/dt)+kx=0
Therefore on solving the above differential equation we get,
x(t)=A₀
where A(t)=A₀
A₀ is the amplitude at t=0 and
is the angular frequency of damped SHM, which is given by,
Now coming to the problem,
Given: m=1.2 kg
k=9.8 N/m
b=210 g/s= 0.21 kg/s
A₀=13 cm
a) A(t)=A₀/8
⇒A₀ =A₀/8
⇒
applying logarithm on both sides
⇒
⇒
substituting the values
b)
, where
is time period of damped SHM
⇒
let be number of oscillations made
then,
⇒